학술논문
Galerkin proper orthogonal decomposition methods for parameter dependent elliptic systems.
Document Type
Journal
Author
Kahlbacher, Martin (A-GRAZ-IMS) AMS Author Profile; Volkwein, Stefan (A-GRAZ-IMS) AMS Author Profile
Source
Subject
35 Partial differential equations -- 35J Elliptic equations and systems
35J25Boundary value problems for second-order elliptic equations
65Numerical analysis -- 65N Partial differential equations, boundary value problems
65N15Error bounds
35J25
65
65N15
Language
English
Abstract
The Galerkin proper orthogonal decomposition (GPOD) methods for parameter dependent elliptic systems, representing powerful techniques for model reductions of linear and nonlinear systems of differential equations, are studied. They are based on a Galerkin type discretization with basis elements created from the system itself. Error estimates for GPOD type approximations for linear and semi-linear elliptic problems are given. The resulting error bounds depend on the number of POD basis functions and on the snapshot grid. Numerical examples are presented.